I hope you excuse the sloppiness of the following description, but I'd like you to realize that only a qualitative approach –instead of a desired quantitative one– is possible. (Otherwise, if you provide the data, I'd be happy).

The question in a pair of words is explain this division line (see bellow the actual question).

Want to see it again? (not so clearly, though)

Or, like here, that line is lower, but still inside Germany and encompassing most Bayern and Baden-Württemberg:

No, seriously, that line doesn't appear only once. I've been browsing some minutes on the AdA, and I find that pattern quite often.

I think it's interesting because one could expect that abrupt division on the boarder of a country, but inside a country is somehow counterintuitive.

Is there an objective argument explaining this rather unexpected behaviour?

I would never call this an unexpected behaviour. The division between High and Low German has been there for centuries, before the current borders existed. I would assume that's the cause of these phenomena. Luther was very important when it comes to the German language, but the German he used was High German, which the people from the north had to learn in order to understand the Bible while the dialects in the south kept evolving on their own. Since I don't have any specific sources (except for Wikipedia) I'll just leave this as a comment.
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clinchMar 5 '14 at 18:25

This line is related to the Benrath Line further north where the linguistic separation of High German (south) and Low German (north) took place.

In the map above it can be seen that the dialects in Alsace (France), Switzerland, South Tyrol (Italy) and Austria are Upper German as well.

High German subdivides into Upper German (green) and Central German (blue), and is distinguished from Low German (yellow) and Dutch. The main isoglosses, the Benrath and Speyer lines, are marked in black.

Germany united very late in history. There are volumes of books about what happened between ~1800 (when Germany consisted of a plethora of small kingdoms, duchies, free citys, and other entities) and 1918, when there was, for the first time, a united german nation. (And it wasn't even clear until after WW1 if Austria should be a state of its own or a part of germany; the winners of the war decided 2 states would be less dangerous that one). This shows a few maps what happened in that time.

But Germany didn't, unlike many other nations, have a central power that defined what "correct" german was. Other nations, like France were much more centralized, trade and cultural exchange happened mostly within the state borders. But for a merchant, in what is now southwest germany, it was much more likely to visit Vienna (along the river Danube) than to visit, for example, Berlin. So, unification of dialects, especially along borders of current nations, just didn't start until about 100 years ago.

The Austro-Prussian War or Seven Weeks' War was a war fought in 1866 between the German Confederation under the leadership of the Austrian Empire and its German allies on one side and the Kingdom of Prussia with its German allies and Italy on the other, that resulted in Prussian dominance over the German states.

The Kingdom of Bavaria and the Kingdom of Württemberg were on the side of Austria while most of the other German Kingsdoms where allies of Prussia.

The close connection between Bavaria and Austria existed for centuries, only the boundaries have shifted over time. The following two maps show that major areas of todays Austria and Bavaria once shared the same government.